16 X 20 prints are definitely better with 8Mp. The largest 16 X 20 crop you can get from an 8Mp shot is just a tad over 150 PPI. That will give a decent print, but there is noticeable deterioration in quality going below that. The point of diminishing returns is about 200PPI, so even 8Mp can be improved. But 150 gives a nice print. If you have a good image editor there are things you can do to improve that a little.
If you are looking for a long telephoto I think in balance the FZ 20 might be a tad better choice than the 8800. It won't give as nice a 16 X 20 by any means, but it is a little more versatile for available light telephoto shots. The FZ 20 maintains f2.8 all the way to 12X where the Nikon drops almost 2 f-stops to f5.2. That uses up most of the advantage of the stabilization in requiring almost 4 times the exposure to get the same shot. If 16 X 20 is a priority for you then the Nikon is the better choice for many situations.
The A200 is a fine camera. Unless your priority is nature photography the wide angle is more useful in everyday photography than the long telephoto IMO. A stabilized 12X zoom is impressive, but so is the capability of wide angle – especially with stabilization. You can shoot at ¼ second in many situations at wide angle with stabilization.
The control setup is also better on the A200 than either of the others. The Nikon has better controls than the FZ 20, but I've never liked Nikon's setup on their higher end prosumer cameras. The A200 has lots of physical controls that are thought out well. The big manual zoom ring is great. I find it especially irritating to have to use a dinky electric zoom with a 10-12X zoom.
The FZs have a great manual focus setup obviously installed by Leica and a handy burst button. Otherwise everything is menu driven. Even my little pocket camera has dedicated controls for things like switching flash modes, macro, spot meter etc that require a trip to the menu on the FZs. You get accustomed to it and it isn't as bad with an EVF, but they could have done better. The EVF nor LCD brighten enough in low light to properly frame a flash shot. The FZ20 focuses fine with the assist light, but you can't see what you are shooting very well. The A200 lets you frame in very low light and focuses well.